Tonality and Transformation (Oxford Studies in Music Theory)

270 Pages·2011·1.74 MB·English

by  Steven Rings

Tonality and Transformation
OXFORD STUDIES IN MUSIC THEORY
Series Editor Richard Cohn
Studies in Music with Text , David Lewin
Music as Discourse: Semiotic Adventures in Romantic Music , Kofi Agawu
Playing with Meter: Metric Manipulations in Haydn and Mozart’s Chamber Music
for Strings, Danuta Mirka
Songs in Motion: Rhythm and Meter in the German Lied, Yonatan Malin
A Geometry of Music: Harmony and Counterpoint in the Extended Common
Practice, Dmitri Tymoczko
In the Process of Becoming: Analytic and Philosophical Perspectives on Form in Early
Nineteenth-Century Music, Janet Schmalfeldt
Tonality and Transformation, Steven Rings
Tonality and Transformation
STEVEN RINGS
1
1
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Library of Congress Cataloging-in-Publication Data
Rings, Steven.
Tonality and transformation / Steven Rings.
p. cm.—(Oxford studies in music theory)
Includes bibliographical references and index.
ISBN 978-0-19-538427-7
1. Music theory. 2. Tonality. 3. Musical intervals and scales. 4. Musical analysis.
I. Title.
MT6.R682T66 2011
781.2—dc22 2010019212
Publication of this book was supported by the AMS 75 PAYS Publication Endowment Fund of the American
Musicological Society.
1 3 5 7 9 8 6 4 2
Printed in the United States of America
on acid-free paper
CONTENTS

Acknowledgments vii
Note to Readers ix
A Note on Orthography x i
Introduction 1
P ART I
Theory and Methodology

Chapter 1: Intervals, Transformations, and Tonal Analysis 9
Chapter 2: A Tonal GIS 41
Chapter 3: Oriented Networks 101
PART II
Analytical Essays

Chapter 4: Bach, Fugue in E major, W ell-Tempered Clavier ,
Book II, BWV 878 151
Chapter 5: Mozart, “Un’aura amorosa” from C osì fan tutte 171
Chapter 6: Brahms, Intermezzo in A major, op. 118, no. 2 185
Chapter 7: Brahms, String Quintet in G major, mvt. ii, Adagio 203
Aft erword 221
Glossary 223
Works Cited 231
Index 239
This page intentionally left blank
ACKNOWLEDGMENTS
Th anks are due fi rst to my wife Gretchen, for her prodigious patience and grace;
though she remains blissfully innocent of this book’s contents, she has been a lim-
itless source of inspiration. My son Elliott served as a sort of inadvertent quality
control: this volume would have been completed at least a year sooner had he not
come along. I hope my thinking is a year more refi ned than it would have been
without him; my life is certainly immeasurably richer. Th e book is dedicated to
them. I also thank my mother Linda, my father Dale, and my brother Mike for
their unwavering love and support.
My Doktorvater Daniel Harrison oversaw the fi rst iteration of many of these
ideas; his spirit imbues this work. David Clampitt introduced me to this style
of music theory and off ered trenchant observations on ideas new to this book.
My other teachers at various stages in my graduate work—in particular, Pat
McCreless, Allen Forte, James Hepokoski, Leon Plantinga, Craig Wright, Michael
Cherlin, and David Damschroder—all played crucial roles in shaping my theo-
retical and critical outlook. Ian Quinn saved me from myself at one very early
stage, pointing out a rather hilarious, exhaustion-induced slip (I had decided for
several pages that there were only 11 chromatic pitch classes). Ramon Satyendra
and Julian Hook both read the manuscript and provided invaluable comments
on matters large and small. Henry Klumpenhouwer off ered critical perspectives
on the conceptual foundations of Lewinian theory, while Peter Smith and Frank
Samarotto lent insight into matters Schenkerian. Dmitri Tymoczko has been a
valued sparring partner and friend; this book has benefi ted greatly from his criti-
cal perspective. Th e anonymous readers for Oxford challenged me on several
important points and forced me to clarify my thinking. Lucia Marchi answered
questions on Da Ponte’s verse. My assistant Jonathan De Souza has done yeoman
work as a design consultant, typeface expert, punctuation cop, indexer, and editor
extraordinaire (his passion for the Chicago Manual almost exceeds my own). All
of these individuals helped improve this book. Th e errors that inevitably remain
are mine, not theirs.
Richard Cohn has been a supporter of this work from the beginning—he has
in many ways opened the theoretical space within which my ideas have unfolded.
As the editor of this series, he also helped acquire the book for Oxford. I cannot
thank him enough. Suzanne Ryan has been a model editor, enthusiastic and
patient in equal measure; her confi dence and understanding helped me weather
a couple rough patches. Norm Hirschy and Madelyn Sutton at Oxford have also
vii
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viii Acknowledgments
been a delight to work with, making the whole process run more smoothly than I
could have hoped. I would also like to thank the Mrs. Giles Whiting Foundation
for supporting the year’s research leave necessary to complete the book, and the
American Musicological Society for a generous subvention from the AMS 75 PAYS
Publication Endowment Fund.
My scholarly home during this book’s writing has been the University of
Chicago. I would like to thank the chairs of the music department during this
time—Robert Kendrick and Martha Feldman, as well as interim chairs Anne
Robertson and Larry Zbikowski—for providing unstinting support and helping
to create the ideal intellectual environment for a junior faculty member. My fel-
low theorists at Chicago—Larry Zbikowski and Th omas Christensen—are the
best professional and intellectual role models I could hope for; they are also good
friends. My colleagues in historical musicology, ethnomusicology, and composi-
tion have at once inspired me with their own achievements and helped to keep my
thinking productively unsettled. Th e same can be said for the remarkable cohort of
graduate students that I have had the pleasure to work with over the last fi ve years.
Finally, I would like to thank Berthold Hoeckner for many hours of stimulating
conversation and for his valued insights into the balance between work and family.
While I cannot imagine a better personal home than the one I described in the
fi rst paragraph of these acknowledgments, I cannot imagine a better intellectual
home than the one created by my friends and mentors in the University of Chicago
Department of Music.
NOTE TO READERS
I have sought to make this book both accessible and formally substantive. It is
a tricky balance: one risks disappointing both specialists (who wish there was
more math) and nonspecialists (who wish there was less). Th e latter readers
may indeed wonder why any math is needed at all.1 While I hope that the
book will speak for itself in this regard, I will answer here that statements in
transformational theory gain their musical suggestiveness in signifi cant part
from the formal structures that support them. Th ose structures situate each
musical interval or gesture within a richly developed conceptual space; the
algebraic contours of that space contribute in important ways to the character
of the interval or gesture in question. Th is underlying formal context is some-
times operative only “behind the scenes”; at other times it is thematized in the
foreground of an analysis. In either case, an awareness of the pertinent under-
lying structure adds considerably to the allusiveness of any observation made in
the theory, sensitizing us to the expressive particularity of a given musical rela-
tionship. Moreover, the theory’s formalism can act as a generator of insights:
once a basic musical observation has been rendered in transformational terms,
the technology can lead the analyst toward new observations. Th e formal pre-
cision of the apparatus assures that the new insights will be related to the old,
oft en in compelling ways.
I have nevertheless limited the amount of formalism in the book, and not
only out of ethical concerns for accessibility. Th e simplicity of the book’s math
results from my conviction that much of the fascination in this style of music
theory resides in the reciprocal interaction that it aff ords between formal ideas and
musical experience. One does not need to delve very far into the math to explore
that interaction. My interest has thus been to employ only as much formalism as
needed, and to expend somewhat greater eff ort seeking out the ways in which the
resulting technical ideas may be brought to bear on musical experience—modeling
or shaping it—in ways that are at once concrete and immediate. For the specialist
wishing for more mathematical development, I hope the basic ideas introduced
1. In addition to my comments here, readers may wish to consult John Clough’s eloquent answer to
this question in his review of David Lewin’s Generalized Musical Intervals and Transformations
( Clough 1989 , 227) .
ix